IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v164y2022ics0960077922008621.html
   My bibliography  Save this article

A Taylor-Splitting Collocation approach and applications to linear and nonlinear engineering models

Author

Listed:
  • Çayan, Seda
  • Özhan, B. Burak
  • Sezer, Mehmet

Abstract

A novel matrix method based on the Taylor series called Taylor-Splitting Collocation Method is presented to solve linear and nonlinear ordinary differential equations. Unlike the previous approaches, the fundamental matrix equation is reformulated using interval splitting. The residual error estimation algorithm is presented. Convergence analysis is given in a general form. Four different mechanical models are analyzed:1.Forced oscillations of a linear spring-mass model2.Forced oscillations of a nonlinear spring-mass model3.Free oscillations of a cubic nonlinear spring-dashpot-mass model4.Forced oscillations of a damped nonlinear pendulum model

Suggested Citation

  • Çayan, Seda & Özhan, B. Burak & Sezer, Mehmet, 2022. "A Taylor-Splitting Collocation approach and applications to linear and nonlinear engineering models," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
  • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008621
    DOI: 10.1016/j.chaos.2022.112683
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922008621
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2022.112683?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Darae Jeong & Yibao Li & Chaeyoung Lee & Junxiang Yang & Yongho Choi & Junseok Kim, 2019. "Verification of Convergence Rates of Numerical Solutions for Parabolic Equations," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-10, June.
    2. Alvaro H. Salas & S. A. El-Tantawy & Noufe H. Aljahdaly, 2021. "An Exact Solution to the Quadratic Damping Strong Nonlinearity Duffing Oscillator," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-8, January.
    3. Berna Bülbül & Mehmet Sezer, 2013. "Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, June.
    4. Oğuz, Cem & Sezer, Mehmet, 2015. "Chelyshkov collocation method for a class of mixed functional integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 943-954.
    5. S. A. El-Tantawy & Alvaro H. Salas & M. R. Alharthi, 2021. "On the Analytical Solutions of the Forced Damping Duffing Equation in the Form of Weierstrass Elliptic Function and its Applications," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-9, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Naserizadeh, L. & Hadizadeh, M. & Amiraslani, A., 2021. "Cubature rules based on a bivariate degree-graded alternative orthogonal basis and their applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 231-245.
    2. Kürkçü, Ömür Kıvanç & Aslan, Ersin & Sezer, Mehmet, 2016. "A numerical approach with error estimation to solve general integro-differential–difference equations using Dickson polynomials," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 324-339.
    3. Balcı, Mehmet Ali & Sezer, Mehmet, 2016. "Hybrid Euler–Taylor matrix method for solving of generalized linear Fredholm integro-differential difference equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 33-41.
    4. Noufe H. Aljahdaly & S. A. El-Tantawy, 2021. "On the Multistage Differential Transformation Method for Analyzing Damping Duffing Oscillator and Its Applications to Plasma Physics," Mathematics, MDPI, vol. 9(4), pages 1-12, February.
    5. Nikooeinejad, Z. & Heydari, M. & Loghmani, G.B., 2022. "A numerical iterative method for solving two-point BVPs in infinite-horizon nonzero-sum differential games: Economic applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 404-427.
    6. Rahimkhani, P. & Ordokhani, Y., 2022. "Chelyshkov least squares support vector regression for nonlinear stochastic differential equations by variable fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    7. Hamid, Muhammad & Usman, Muhammad & Haq, Rizwan Ul & Tian, Zhenfu, 2021. "A spectral approach to analyze the nonlinear oscillatory fractional-order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    8. Ali, Irfan & Masood, W. & Rizvi, H. & Alrowaily, Albandari W. & Ismaeel, Sherif M.E. & El-Tantawy, S.A., 2023. "Archipelagos, islands, necklaces, and other exotic structures in external force-driven chaotic dusty plasmas," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008621. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.